2009/10/13 by C.W. Leung, C. W. Leung, Leung, C. W. +6
Mathematics · #46H40 #46L08 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA #msc:46H40 #msc:46L08
paper · pdf · doi:10.48550/arxiv.0910.2335
9 pages
arxiv created 2009/10/13 · openalex publication_date 2009/10/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be a C^*-algebra. Let E and F be Hilbert A-modules with E being full. Suppose that θ: E→ F is a linear map preserving orthogonality, i.e., <θ(x), θ(y) > = 0 whenever <x, y > = 0. We show in this article that if, in addition, A has real rank zero, and θ is an A-module map (not assumed to be bounded), then there exists a central positive multiplier u∈ M(A) such that <θ(x), θ(y) > = u < x, y> (x,y∈ E). In the case when A is a standard C^*-algebra, or when A is a W^*-algebra containing no finite type II direct summand, we also obtain the same conclusion with the assumption of θ being an A-module map weakened to being a local map.